Question

Consider the following formulas with all the symbols having their usual meanings:

(a) \({P_t} = {P_c}\left( {1 + \frac{m}{2}} \right)\)

(b) \({I_t} = {I_c}{\left( {1 + \frac{{{m^2}}}{2}} \right)^{\frac{1}{2}}}\)

(c) \({P_t} = {P_c}\left( {1 + \frac{{{m^2}}}{2}} \right)\)

(d) \({I_t} = {I_c}{\left( {1 + \frac{m}{2}} \right)^{\frac{1}{2}}}\)

Which of the above are incorrect?

1. (a) and (b) 
2. (b) and (c) 
3. (c) and (d) 
4. (a) and (d)

Answer 1

Correct Answer - Option 4 : (a) and (d)

The total transmitted power for an AM system is given by:

\({P_t} = {P_c}\left( {1 + \frac{{{m^2}}}{2}} \right)\)

Pt = It2 R (Transmitted Power)

PC = IC2 R (Carrier Power)

m = Modulation index

It = RMS value of the antenna current after modulation

IC = RMS value of the antenna current before modulation

R = Antenna Resistance

∴ The antenna current of modulated and unmodulated signals are related as:

\(I_t^2R=I_C^2R​​​​\left( {1 + \frac{{{m^2}}}{2}} \right)\)

\({I_t} = {I_C}\sqrt {1 + \frac{{{m ^2}}}{2}} \)

∴ Statements (a) and (d) are incorrect.